Questions and Answers
What is a variable?
What is an algebraic expression?
An expression that contains at least one variable and does not contain an equal sign.
What is a term in an algebraic expression?
Part of an algebraic expression that can be a number, a variable, or a product of both.
What does it mean to evaluate an expression?
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What does it mean to substitute in an algebraic expression?
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What does it mean to simplify an expression?
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What are like terms?
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What is a coefficient?
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What are equivalent expressions?
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What does it mean to expand an expression?
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What does it mean to factor an expression?
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What is the sum?
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What is the difference?
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What is the product?
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What is the quotient?
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Study Notes
Algebraic Expressions Overview
- Variable: A letter representing a quantity that can change. Example: In "2x + 1", x is a variable.
- Algebraic Expression: An expression containing at least one variable and no equal sign. Examples include "3y - 2" and "4y".
Key Components of Algebraic Expressions
- Term: A part of an algebraic expression, which can be a number, a variable, or a combination of both. Example: In "2x + 14", terms are 2x and 14.
- Coefficient: The numerical factor in a term of an expression. Example: In "8z", the coefficient is 8.
- Like Terms: Terms that share the same variables and corresponding exponents. They can be combined. Example: In "2x + 4 + x + 1", 2x and x are like terms.
Operations with Algebraic Expressions
- Evaluate: The process of finding the value of an expression.
- Substitute: Replacing a variable with a specific number.
- Simplify: Writing an equivalent expression by combining like terms.
Expression Relationships
- Equivalent Expressions: Expressions that are equal for all values of the variables. Example: "5x + 7x" and "12x" are equivalent.
- Expand: Writing an expression without parentheses. Example: 4(y + 1) becomes 4y + 4.
- Factor: Writing an expression that uses parentheses. Example: 4x + 4 can be factored to 4(x + 1).
Basic Mathematical Terms
- Sum: The result of an addition problem.
- Difference: The result of a subtraction problem.
- Product: The result of a multiplication problem.
- Quotient: The result of a division problem.
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Description
Explore key concepts from Algebra Chapter 7 with these flashcards. Learn about variables, algebraic expressions, and terms to strengthen your understanding of algebraic foundations. Perfect for review and study before exams.
